Characteristics of truncation resonances in periodic bilayer rods and beams with symmetric and asymmetric unit cellsa)

Abstract

Truncation resonances are resonant frequencies that occur within bandgaps and are a prominent feature of finite phononic crystals. While recent studies have shed light on the existence conditions and modal characteristics of truncation resonances in discrete systems, much remains to be understood about their behavior in continuous structures. To address this knowledge gap, this paper investigates the existence and modal characteristics of truncation resonances in periodic bilayer beams, both numerically and experimentally. Specifically, the effect of symmetry of the unit cells, boundary conditions, material/geometric properties, and the number of unit cells are studied. To this end, we introduce impedance and phase velocity ratios based on the material and geometric properties and show how they affect the existence of truncation resonances, relative location of the truncation resonances within the bandgap, and spatial attenuation or degree of localization of the truncation resonance mode shapes. Finally, the existence and mode shapes of truncation resonances are experimentally validated for both longitudinal and flexural cases using three-dimensional (3D) printed periodic beams. This paper highlights the potential impact of these results on the design of finite phononic crystals for various applications, including energy harvesting and passive flow control.